A study of clusters is presented by means of the function Nm(θ), i.e. the total number N of members heavier than a limiting mass m, as a function of the limiting projected angular distance from the centre θ. As a rule such a function is found to possess a well-defined maximum change of slope - an apparent Ȝdeflectionȝ - if the limiting mass is large enough (see Figure 1 a-g). Some possible definitions of this deflection and the corresponding special Ȝcore radiusȝ of the cluster are described elsewhere (Astrofizika, 7, 435, 1971). the typical occurrence and rather regular behaviour (systematic temporal variations) of this deflection in a sample of 17 configurations simulated by S.J. Aarseth and S.D.M. White for different conditions prove this feature to be a natural consequence of the gravitational interaction of many bodies in a statistical sense; it is apparently a characteristic of core formation and the evolution of clusters. in the case of computer data the existence of such deflections cannot possibly be due to any observational error or uncertainty or erroneous personal judgement. the corresponding diagrams, Nm(θ) for clusters of galaxies (see also loc. cit.) are found to be practically indistinguishable from those of star clusters and simulated systems. They show the very same type of deflection, the same remarkably small dependence on the choice of the limiting mass, that of the Ȝcentreȝ, the field correction etc. As simulations give just the same diagrams as have been obtained observationally it is plausible to regard also these observational findings as dynamically necessary and not chance coincidences, unless the actual clusters of galaxies are stabilized by some continuously distributed intergalactic Ȝhidden matterȝ instead of the masses of observable discrete bodies themselves. However one can hardly accept a radically different explanation for the apparently identical phenomenon in the case of systems of galaxies on the one hand and those of stars on the other. Estimates of the crossing time tc of the systems together with morphological arguments and numerical experiments indicate that actual “rich” clusters of galaxies might typically be near a particular epoch of very rapid systematic cosmological evolution. A considerable decrease of the aforementioned “core radii” (a transition between two nearly constant values) with the other characteristic sizes of the systems almost unchanged (Figure 1 a-d). the corresponding phenomena were detected earlier observationally and consequently these empirical data, together with their consequences, now seem to be once again corroborated (see e.g. Astron. Nachrichten, 297, 311, 1976). These remarkable analogies suggest that a similar mechanism is responsible for the formation and evolution of conspicuous cores of clusters and a similar solution of the somewhat controversial situation with regard to mass segregation both for clusters of galaxies and open star clusters (e.g. by properly choosing the initial conditions).